Romans 11:11 introduces a long discourse showing that we should not consider as lost those not currently headed toward salvation. The Bible provides ample evidence of two more periods of salvation ahead. This first of these times of judgment will occur during the Millennium. It will be primarily directed toward Israel and spread from there to other nations. The second period will include all who never had an opportunity for salvation when they first lived, when God simply passed over them, consigning or ordaining them to stumble. This will not commence until after the Millennium (Revelation 20:11-15).
Paul continues to expand this thought in verses 11-14, explaining that God's rejection of Israel is only temporary. He intends His rebuff of them to open the way to include Gentiles in all the promises given to Abraham. When Israel becomes aware of what has happened to them and the Gentiles because of their stumbling, it will work to remove their complacency and motivate them to obey God.
In verses 15-16, Paul lays the groundwork for indicating a time in the future when all Israel will be reconciled to God: "For if their being cast away is the reconciling of the world, what will their acceptance be but life from the dead? For if the firstfruit is holy, the lump is also holy; and if the root is holy, so are the branches." In other words, those God has cast away at this time (Israelites, the natural branches) will be drawn to Him at some future time and regrafted into the tree. The firstfruit is the church. We are holy and already part of the holy tree, the Family of God. When God regrafts Israel into the tree, they, too, will be holy because we will all be connected to the same root, Christ (John 15:1-5).
The Bible affords those of us called now not even the slightest room for pride because only God knows the reasons for His mercy toward us. Such scriptures as I Corinthians 1:26-29 make it plain that it is certainly not because we are better than others are. God intends that we be humbled by understanding our privilege in having such an awesome gift fall into our laps, and be motivated to respond to Him in submission to His commandments. We do this by showing the same kindness, tenderness, and mercy to others whether or not they have also received this gracious gift.